scholarly journals A mathematical modeling for the lookback option with jump–diffusion using binomial tree method

2011 ◽  
Vol 235 (17) ◽  
pp. 5140-5154 ◽  
Author(s):  
Kwang Ik Kim ◽  
Hyun Suk Park ◽  
Xiao-song Qian
Keyword(s):  
Mathematical Modeling ◽  
Jump Diffusion ◽  
Binomial Tree ◽  
Lookback Option ◽  
Tree Method

Convergence of the Binomial Tree Method for American Options in a Jump-Diffusion Model

2005 ◽  
Vol 42 (5) ◽  
pp. 1899-1913 ◽  
Author(s):  
Xiao-song Qian ◽  
Cheng-long Xu ◽  
Li-shang Jiang ◽  
Bao-jun Bian
Keyword(s):  
Diffusion Model ◽  
American Options ◽  
Jump Diffusion ◽  
Binomial Tree ◽  
Jump Diffusion Model ◽  
Tree Method

scholarly journals A New Binomial Tree Method for European Options under the Jump Diffusion Model

2019 ◽  
Vol 07 (12) ◽  
pp. 3012-3021
Author(s):  
Lingkang Zhu ◽  
Xiu Kan ◽  
Huisheng Shu ◽  
Zifeng Wang
Keyword(s):  
Diffusion Model ◽  
Jump Diffusion ◽  
European Options ◽  
Binomial Tree ◽  
Jump Diffusion Model ◽  
Tree Method

Option Pricing in a Jump-Diffusion Model with Regime Switching

2009 ◽  
Vol 39 (2) ◽  
pp. 515-539 ◽  
Author(s):  
Fei Lung Yuen ◽  
Hailiang Yang
Keyword(s):  
Diffusion Model ◽  
Regime Switching ◽  
Jump Diffusion ◽  
Mathematical Finance ◽  
Extended Model ◽  
Exotic Options ◽  
Switching Model ◽  
Jump Diffusion Model ◽  
Trinomial Tree ◽  
Tree Method

AbstractNowadays, the regime switching model has become a popular model in mathematical finance and actuarial science. The market is not complete when the model has regime switching. Thus, pricing the regime switching risk is an important issue. In Naik (1993), a jump diffusion model with two regimes is studied. In this paper, we extend the model of Naik (1993) to a multi-regime case. We present a trinomial tree method to price options in the extended model. Our results show that the trinomial tree method in this paper is an effective method; it is very fast and easy to implement. Compared with the existing methodologies, the proposed method has an obvious advantage when one needs to price exotic options and the number of regime states is large. Various numerical examples are presented to illustrate the ideas and methodologies.

scholarly journals PENENTUAN HARGA KONTRAK OPSI KOMODITAS EMAS MENGGUNAKAN METODE POHON BINOMIAL

2017 ◽  
Vol 6 (2) ◽  
pp. 99
Author(s):  
I GEDE RENDIAWAN ADI BRATHA ◽  
KOMANG DHARMAWAN ◽  
NI LUH PUTU SUCIPTAWATI
Keyword(s):  
Option Prices ◽  
European Option ◽  
Binomial Tree ◽  
Call Options ◽  
Option Contracts ◽  
Put Option ◽  
Black Scholes ◽  
Tree Method

Holding option contracts are considered as a new way to invest. In pricing the option contracts, an investor can apply the binomial tree method. The aim of this paper is to present how the European option contracts are calculated using binomial tree method with some different choices of strike prices. Then, the results are compared with the Black-Scholes method. The results obtained show the prices of call options contracts of European type calculated by the binomial tree method tends to be cheaper compared with the price of that calculated by the Black-Scholes method. In contrast to the put option prices, the prices calculated by the binomial tree method are slightly more expensive.

TREE METHOD FOR OPTION PRICING UNDER STOCHASTIC VARIANCE

2000 ◽  
Vol 03 (03) ◽  
pp. 557-557
Author(s):  
DRAGAN ŠESTOVIĆ
Keyword(s):  
Option Pricing ◽  
Asset Price ◽  
Three Dimensional ◽  
Diffusion Limit ◽  
Lattice Method ◽  
Binomial Tree ◽  
Long Run ◽  
Hedging Portfolio ◽  
Risk Neutral Probabilities ◽  
Tree Method

We develop a recombining tree method for pricing of options by using a general two-factor stochastic-variance (SV) diffusion model for asset price dynamics. We show that it is possible to construct a riskless hedge by including additional short-term options in the hedging portfolio. This procedure gives us Partial Differential Equation (PDE) that can be solved by using standard numerical techniques giving us a unique option's price. We show that the option's price does not depend on the long run volatility forecast but only on the parameters of the model, which are related to the volatility of variance. We show one particular transformation of PDE to the Finite Difference Equation (FDE) that leads to the three-dimensional lattice method similar to the standard binomial-tree method. Our tree grows in the price-variance space and similarly to the binomial-tree, the coefficients of the FDE can be interpreted as risk neutral probabilities for jumping between the tree nodes. By investigating an error accumulation in the tree we found the stability criterion and the method that can be applied in order to achieve a stabile procedure. Our option pricing method can be used for European and American options and various payoffs. Since the procedure converges quickly and can be easily implemented, we believe that it could be useful for practitioners. The SV model we used here was shown earlier to be a diffusion limit of various GARCH-type models giving the possibility of using parameters obtained in the discrete-time GARCH framework as an input for our option pricing method.

Pricing S&P500 barrier put option of American type under Heston–CIR model with regime-switching

2019 ◽  
Vol 06 (02) ◽  
pp. 1950014 ◽  
Author(s):  
Farshid Mehrdoust ◽  
Idin Noorani
Keyword(s):  
Expectation Maximization ◽  
Regime Switching ◽  
Likelihood Estimation ◽  
Least Square ◽  
Hidden Markov Chain ◽  
Cir Model ◽  
Binomial Tree ◽  
Put Option ◽  
Rate Processes ◽  
Tree Method

In this paper, we consider the regime-switching Heston–CIR model, where the parameters of the volatility process are modulated by a Hidden Markov chain and the unobserved regimes. Then, we calibrate the parameters of the volatility and interest rate processes by the expectation maximization (EM) and maximum likelihood estimation (MLE) algorithms, respectively. Next, we use the least square Monte-Carlo (LSM) algorithm to determine the S&P500 American barrier put option under the Heston–CIR model. Finally, by the binomial tree method as a benchmark, we provide some numerical experiments to illustrate the accuracy of the achieved results.

scholarly journals Optimal Exercise Boundary of American Fractional Lookback Option in a Mixed Jump-Diffusion Fractional Brownian Motion Environment

2017 ◽  
Vol 2017 ◽  
pp. 1-17 ◽  
Author(s):  
Zhaoqiang Yang
Keyword(s):  
Brownian Motion ◽  
Stock Price ◽  
Jump Diffusion ◽  
Fundamental Solutions ◽  
Early Exercise ◽  
Optimal Exercise Boundary ◽  
Lookback Options ◽  
Exercise Price ◽  
Lookback Option ◽  
Exercise Boundary

A new framework for pricing the American fractional lookback option is developed in the case where the stock price follows a mixed jump-diffusion fraction Brownian motion. By using Itô formula and Wick-Itô-Skorohod integral a new market pricing model is built. The fundamental solutions of stochastic parabolic partial differential equations are estimated under the condition of Merton assumptions. The explicit integral representation of early exercise premium and the critical exercise price are also given. Numerical simulation illustrates some notable features of American fractional lookback options.

Entropy binomial tree method and calibration for the volatility smile

2020 ◽  
Vol 28 (11) ◽  
pp. 1591-1608
Author(s):  
Wenxiu Gong ◽  
Zuoliang Xu ◽  
Qinghua Ma
Keyword(s):  
Volatility Smile ◽  
Binomial Tree ◽  
Tree Method
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